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9th grade · Math · Unit 16 of 16

Rearranging Formulas

Solve for any letter

What your child practices

Rearranging a formula to solve for one quantity (d = rt for t, P = 2l + 2w for l) and using it, plus justifying each step in solving an equation.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.12(E) · solving formulas and literal equations for a variable

How we explain it

Children can open this short lesson before they practice.

  1. Treat the other letters like numbers.
  2. Undo each operation on the letter you want, in reverse order.
  3. Do the same thing to both sides.

Example: Solve d = rt for t. t is multiplied by r. Divide both sides by r. Answer: t = d/r

Rearranging Formulas in Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 16 of 16 in 9th grade Math, after Sequences.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Texas Education Agency (TEA)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    To solve 8x + 6 = 54, Jay first subtracts 6 from both sides. What equation comes next?

    • 8x = 54
    • 8x = 48
    • 8x = 60
    • x + 6 = 54

  2. Question 2

    Use P = 2l + 2w. A rectangle has perimeter 42 ft and width 11 ft. What is its length?

    • 21 ft
    • 31 ft
    • 20 ft
    • 10 ft

  3. Question 3

    Solve C = 2πr for r.

    • r = C − 2π
    • r = 2πC
    • r = C/(2π)
    • r = 2π/C

  4. Question 4

    Solve A = ½bh for h.

    • h = 2b/A
    • h = A/(2b)
    • h = A − ½b
    • h = 2A/b

  5. Question 5

    To solve 3x + 6 = 21, Leo first subtracts 6 from both sides. What equation comes next?

    • 3x = 27
    • 3x = 21
    • 3x = 15
    • x + 6 = 8

  6. Question 6

    Use d = rt. A car travels 90 miles at 15 miles per hour. How many hours does it take?

    • 9 h
    • 6 h
    • 1350 h
    • 7 h

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